On the absorption by near-extremal black branes

We study the absorption of a minimally coupled scalar in the gravitational background created by a stack of near-extremal black three-branes, and more generally by M2-, M5- and Dp-branes. The absorption probability has the form P(l)=P0(l)fl(λ), where P0(l) is the partial wave's absorption probability in the extremal case, and the thermal factor fl(λ) depends on the ratio of the frequency of the incoming wave and the Hawking temperature, λ=ω/πT. Using Langer-Olver's method, we obtain a low-temperature (λ>>1) asymptotic expansion for P(l) with coefficients determined recursively. This expansion, which turns out to be a fairly good approximation even for λ∼1, accounts for all power-like finite-temperature corrections to P0(l), and we calculate a few terms explicitly. We also show that at low temperature the absorption probability contains exponentially suppressed terms, and attempt to develop an approximation scheme to calculate those. The high-temperature expansion is also considered. For the s-wave, the low-temperature gravity result is consistent with the free finite-temperature field theory calculation, while for high temperature and higher partial waves we find a disagreement. As a check of the approximation methods used, we apply them to the D1-D5-brane system, and compare results to the known exact solution